acoustic loss mechanisms in leaky saw resonators on lithium...

1517 ieee transactions on ultrasonics ferroelectrics and frequency control vol 48 no 6 november 2001

Acoustic Loss Mechanisms in Leaky SAW Resonators on Lithium Tantalate Julius Koskela Jouni V Knuuttila Tapani Makkonen Member IEEE

Victor P Plessky Member IEEE and Martti M Salomaa Member IEEE

AbstractmdashWe discuss acoustic losses in synchronous leaky surface acoustic wave (LSAW) resonators on rotated Y-cut lithium tantalate (LiTaO3) substrates Laser probe measurements and theoretical models are employed to idenshytify and characterize the radiation of leaky waves into the busbars of the resonator and the excitation of bulk acousshytic waves Escaping LSAWs lead to a significant increase in the conductance typically occurring in the vicinity of the resonance and in the stopband but they do not explain the experimentally observed deterioration of the electrical reshysponse at the antiresonance At frequencies above the stopshyband the generation of fast shear bulk acoustic waves is the dominant loss mechanism

I Introduction

Lsaw devices operating at radio frequencies are widely employed in modern telecommunication systems In

particular LSAW resonators on rotated Y-cut LiTaO3 and lithium niobate (LiNbO3) substrates constitute building blocks for resonator filters such as impedance element filshyters (IEFs) In the IEFs the resonator performance at frequencies close to the resonance and the antiresonance determines the insertion loss of the device Consequently identifying the leakage mechanisms and minimizing the resonator losses is of major technological and commercial interest In this paper we consider losses in LSAW resshyonators on LiTaO3 substrates LSAW on 36-42YX-LiTaO3 contain a small slow shear

bulk acoustic wave (ss-BAW) component that results in an attenuation of the LSAW Significant reduction in this propagation loss was achieved with the discovery [1] that the coupling to ss-BAWs may be diminished by an optimal combination of the crystal cut angle and the thickness of the aluminum electrodes However a remaining problem is that LSAW resonators feature strong frequency-dependent losses which lead to reduction in the filter performance

Manuscript received July 6 2000 accepted March 16 2001 This research is supported by TEKES (Technological Development Censhytre Finland) and the Helsinki University of Technology J Koskela J V Knuuttila and T Makkonen acknowledge the Academy of Finshyland for Fellowships within the Graduate School in Technical Physics J Koskela and J V Knuuttila further thank the NOKIA Foundation for Research Scholarships J Koskela J V Knuuttila T Makkonen and M M Salomaa are

with the Materials Physics Laboratory Helsinki University of Techshynology (Technical Physics) FINndash02015 HUT Finland Current adshydress of J Koskela Nokia Research Center FINndash00045 Nokia Group Finland (e-mail MarttiSalomaahutfi) V P Plessky is with Thales Microsonics (formerly Thomson Mishy

crosonics) SAW Design Bureau CHndash2000 Neuchatel Switzerland

860 880 900 920 940 96010-4

10-3

10-2

10-1

100

Adm

ittan

ce

[1 Ω

] |Y( f )|

Re Y( f )

experiment theory

f [MHz]

Fig 1 Admittance and conductance of a synchronous test resonator on 36YX-cut LiTaO3 vs a one-dimensional resonator model [8] Despite including a series resistance as high as 05 Ω the modeled conductance ie the losses are too low

and require corrections in the device design [2] Although the role of phenomena such as backscattering into fast shear bulk acoustic waves (fs-BAW) and the synchronous excitation of fs-BAWs have been studied [3] the mechashynisms underlying the losses are for the moment not well understood Our recent measurements [4] with a scanning optical

Michelson laser interferometer [5] have revealed qualitashytively that strong radiation of LSAWs from the active resshyonator region to the busbars of the device may occur at stopband frequencies [6] Preliminary results of this work were reported in [7] In this paper we characterize the freshyquency dependence and the magnitude of the losses caused by the busbar radiation LSAW coupling to the ss-BAW and the generation of fs-BAWs The laser interferometric measurements of a test resshy

onator are discussed in Section II and the loss mechanisms are analyzed in Section III A phenomenological structure model is constructed in Section IV and the results are presented in Section V Section VI concludes the paper

II Laser Interferometric Measurements

Fig 1 shows the admittance of a synchronous resonator on 36YX-cut LiTaO3 substrate The test device has Np

c0885ndash3010$1000 copy 2001 IEEE


= 120 electrode pairs in the interdigital transducer (IDT) and Ng = 50 electrodes in each reflector The pitch is p = 2214 microm the aperture is W = 70 microm the relative alushyminum electrode thickness is hλ0 = 56 and the metshyallization ratio is about 05 Also shown is a fit to a oneshydimensional phenomenological resonator model [8] which takes into consideration the interactions between LSAWs and fs-BAWs The results are rather typical for the model and LSAW resonators on 36-42YX-LiTaO3 Although the resonance and the dispersion characterisshy

tics are satisfactorily reproduced by the model systematic discrepancies in the conductance representing losses may be observed on the high frequency side of the resonance peak and in the middle of the stopband As the most noshytable consequence the predicted Q value of the antiresoshynance is too high Yet the agreement shown in Fig 1 reshyquires the inclusion of a parasitic series resistance of about 05 Ω a reasonable theoretical estimate would be about one order of magnitude lower Minor differences between the model and the experiments may be explained by the numerous approximations underlying our model but the magnitude of the disagreement rather suggests the exisshytence of additional loss mechanisms To study directly the acoustic activity in LSAW devices

we utilize a scanning optical Michelson interferometer [5] which detects the shear vertical component of the mechanshyical displacement field Fig 2 displays the light reflection data and a wide amplitude scan of the test resonator at the frequency f = 910 MHz coinciding with the unpreshydicted lump in the conductance slightly above the resoshynance peak The resonator is aligned with the crystal Xshyaxis In the longitudinal device direction the acoustic field

remains confined into the active device region as exshypected on the basis of one-dimensional models However the waves are capable of escaping from the device to the busbars At least three separate loss mechanisms may be identified the radiation of LSAWs to the busbars [6] synchronous waveguide radiation of Rayleigh waves [9] at an angle of about 40 and transverse excitation of Rayleigh waves Note that because Rayleigh waves have strong shear vertical polarization and LSAWs are essenshytially shear horizontal surface waves the probe images are likely to strongly pronounce the former over the latter Furthermore it should be kept in mind that mechanisms such as ss-BAW radiation into the bulk and resistive and viscous losses are not revealed from surface scans The observed asymmetry of the probed acoustic field

may be explained by the crystalline anisotropymdashan inshyherent materials propertymdashof the LiTaO3 substrate The LSAW velocity is a symmetric function of the propagation angle θ about the crystal X axis see Fig 2(a) However the LSAW polarization is an asymmetric function of θ and the asymmetry is particularly strong in the shear vertical component detected by the probe [6] The series of probe images in Fig 3 illustrates the deshy

pendence of the LSAW busbar radiation on frequency Below the resonance frequency the phenomenon exists

Fig 2 Areal scan of the test resonator a) Light reflection data b) the shear vertical displacement field at 910 MHz indicating three twoshydimensional leakage mechanisms The displacement is not to scale in the areas with different light reflection coefficients

weakly at frequencies slightly above the resonance it is very pronounced Close to a quenching frequency of about 918 MHz the radiation becomes strongly suppressed and practically disappears Similar frequency dependence may be recognized in the losses in Fig 1 and it may be unshyderstood on the basis of the curvature of loaded slowness curves as will be discussed subsequently

Because of the quenching of the LSAW busbar radiashytion the phenomenon is not likely to be responsible for the residual losses in the middle of the stopband Fig 4 shows the probed field in the resonator at the antiresoshynance In the image the radiation of obliquely propagatshying and transverse Rayleigh waves appear to be the most prominent acoustic loss mechanisms

1519 koskela et al acoustic loss mechanisms

Fig 3 Areal scans of the test resonator featuring the frequency dependence of the LSAW radiation to the busbars Below the resoshynance the radiation is weak (a b) Strong spatially asymmetric radishyation occurs slightly above the resonance (c d) Toward a quenching frequency of about 918 MHz the radiation decreases (e) and virtually disappears (f ) Also scattering from a point-like imperfection in the metallization not related to the busbar radiation is distinguishable

Fig 4 Areal scan of the test resonator at 934 MHz close to the antiresonance frequency

III Theoretical Analysis

Greenrsquos function techniques were employed to anashylyze surface acoustic waves (SAWs) LSAWs1 and bulk acoustic waves (BAWs) on uniformly metallized 36- and 42YX-cut LiTaO3 surfaces With the exception of LSAW attenuation the two cuts are almost identical the results presented here are for the 42-cut The material paramshyeters for the substrate were taken from [10] aluminum was assumed isotropic with a density of 2600 kgm3

and the Lame coefficients micro = 25middot1010 Nm2 and λ = 61middot1010 Nm2

A Leaky Waves on Metallized Crystal Surface

The LSAW slowness under an ideally conducting unishyform metal layer depends on the propagation direction θ and the product of the frequency f and the film thickness h The slowness curves and the attenuation for various frequency-thickness products on 42YX-cut LiTaO3 are depicted in Fig 5 The LSAW polarization is dominantly shear horizontal and the LSAW attenuation is determined by the weak coupling to the ss-BAWs The slowness curves feature both convex and concave

regions implying that the direction of the energy flow varies significantly with the propagation angle To the preshycision of the numerical calculations the LSAW velocity and attenuation under a finite aluminum layer remain symshymetric about the crystal X-axismdashdespite the asymmetry of the LSAW polarization both on free surface and under infinitely thin metallization [6] Leaky waves attenuate because of the coupling of surshy

face waves to ss-BAWs For propagation along X (θ = 0) the attenuation has been shown to depend strongly on the film thickness [1] In the 36-cut the attenuation grows with increasing film thickness whereas in the 42shycut it decreases for hf asymp 780 ms However according to our results the attenuation increases drastically with the propagation angle for both crystal cuts and for all film thicknesses as shown for the 42-cut in Fig 5(b) This beshyhavior is very different from that of Rayleigh waves and it suggests that high order transverse waveguide modes are likely to possess heavy propagation losses

B Leaky Wave Radiation to Busbars

The strong frequency dependence of the LSAW radiashytion to the busbars may be qualitatively understood on the basis of the curvature of the LSAW slowness curves As illustrated in Fig 6 these may be characterized by two thresholds the slowness for X-propagating LSAW sm0 and the maximum x-component of the slowness sm1 Both slowness thresholds are functions of the frequencyshythickness product hf

1Mathematically LSAWs are presented here by the poles of the relevant Greenrsquos function which has been analytically continued [11] to complex-valued slownesses


Fig 5 a) Slowness curves and b) attenuation for LSAWs on unishyformly metallized 42YX-LiTaO3 substrate for thickness-frequency products hf ranging from 0 to 500 ms Dotted and solid curves rigorous calculation and the empirical model from Section IV reshyspectively Dashed curves and circles the slowness curve for fs-BAWs with their energy propagating along the crystal surface rigorous calshyculation and the empirical model respectively

At the stopband frequencies the standing wave field in the resonator satisfies the Bragg condition such that the wavenumbers of the dominating Fourier components along X are kx = plusmnπp with p denoting the mechanical periodicity Consequently the counterpropagating waves forming the standing field have the x slownesses

sx = plusmn1(2pf) (1)

Because the busbars are of uniform metal synchronous radiation of the LSAWs into the busbars is possible if the metallized crystal surface supports propagating eigenshymodes with the same x slowness [Fig 7(a)] Comparing the standing field slowness sx with the threshold slownesses sm0 and sm1 three radiation regimes are identified

Fig 6 Schematic LSAW slowness curve Depending on the slowness along X there may exist two (weak radiation regime I) four (strong radiation regime II) or no (radiation free regime III) LSAW modes

1 Weak Radiation Regime (I) For |sx| lt sm0 the metshyallized surface supports a pair of LSAW eigenmodes with transverse slownesses plusmn |sy| Consequently synchronous busbar radiation is allowed but because the correspondshying transverse wavenumbers are fairly large the coupling to the field in the resonator is weak

2 Strong Radiation Regime (II) For sm0 lt |sx| lt sm1 the metallized surface features two pairs of LSAW eigenshymodes which merge into one pair as |sx| rarr sm1 For |sx| sim sm0 the transverse slownesses are very small for one of the pairs and acoustic energy propagates almost parallel to the crystal X-axis Hence the coupling to the standing wave field in the active region may be considershyable and pronounced LSAW radiation to the busbars is expected The strength of the excitation depends on the structure

3 Radiation Free Regime (III) For |sx| gt sm1 there are no LSAW eigenmodes on a metallized surface Synshychronous busbar radiation is prohibited but weak nonshysynchronous radiation may occur This reasoning results in an important conclusion Beshy

cause the standing field slowness sx is inversely proporshytional to fp and the threshold slownesses are monotonic functions of hf corresponding frequency regimes of radiashytion may be determined The relative threshold frequencies obtained only depend on the relative film thickness h2p in the busbarsmdashthey are independent of for example the shape and the width of the electrodes The results are shown in Fig 7(b) for the 42-cut those

for the 36-cut are almost identical For the metallization thickness and the pitch of the test structure an upper threshold frequency of about 9167 MHz is predicted This agrees well with both the laser interferometric images and the parasitic conductance observed in Fig 1 Indeed the former comparison also confirms that the radiation in the weak radiation regime is very weak


Fig 7 a) Synchronous LSAW busbar radiation from the resonator and b) estimated relative stopband frequencies ffB prone to it as a function of the relative metal thickness h(2p) Here fB denotes the bulk-wave threshold frequency vB2p with vB = 42265 ms

We emphasize that the analysis presented is limited to the stopband frequencies Outside the stopband the analshyysis must be based on the dispersion curve of the LSAW eigenmodes In finite structures small nonsynchronous LSAW radiation to the busbars may also occur Numerical simulations of the effect of the radiation on the electrical response are presented in Section IV

C Rayleigh Waves and BAW

Rayleigh waves may be radiated synchronously to the busbars in the same way as LSAWs [9] The analysis is similar to that just described except that the Rayleigh wave velocity depends only weakly on the propagation anshygle and the aluminum thickness In agreement with the laser probe results a phase (and energy) direction with an angle of about 40is estimated for synchronously coupled SAWs in the stopband of the test resonator The transverse beams seen in Fig 2 and 4 are probashy

bly generated by the transverse electric fields in the end gaps between the busbars and the electrodes However inshycreased radiation seems to originate also from the maxima of the field profile inside the resonator this may be due to the scattering of LSAWs off the ends of the electrodes The range of the beams vastly exceeds the surface region shown in the figures Consequently the beams must be

surface waves Because only Rayleigh waves are theoretshyically predicted to exist in this direction the beams are identified as transversely excited Rayleigh waves ss-BAWs are radiated into the substrate at all freshy

quencies of interest The synchronous radiation of fs-BAWs occurs at high frequencies The slowness curve for surface-skimming fs-BAWs is similar to those of LSAWs with the threshold slownesses sB0 asymp2366middot10minus4 sm and sB1 asymp2501middot10minus4 sm Consequently off-axis synchronous fs-BAW radiation is in principle possible for frequencies above 0946fB about 903 MHz in the test device Howshyever the much stronger on-axis synchronous fs-BAW radishyation will start at 9545 MHz in this device as is evident in Fig 1

IV Phenomenological Model

The preceding analysis is useful for qualitative analysis of the origin and the frequency dependence of the losses but a model is required to study the leakage mechanisms quantitatively Because a rigorous simulation of a realistic resonator structure would require immense computational efforts we resort to a phenomenological model with conshysiderable computational simplification but yet covering the loss mechanisms of main interest LSAW backscattering into fs-BAWs busbar radiation and synchronous fs-BAW excitation ss-BAWs are included only through the LSAW attenuation Although LSAWs on LiTaO3 contain weak longitudinal

and shear vertical components they are essentially shear horizontal surface waves The shear horizontal component features almost symmetric magnitude and weak linearly deviating phase shift as functions of the propagation anshygle [6] Such behavior has been pointed to lead to a shift of the acoustic transduction amplitude with respect to the electric source [12] but here the effect is rather weak about 012 wavelengths The shear vertical displacement profiles in Fig 2 through 4 indicate considerable transshyverse asymmetry but our primitive calculations for vanshyishing metal thickness imply that the dominating shear horizontal field is nevertheless almost symmetric [6] This suggests that for rough evaluation it suffices to consider the shear horizontal component only and to treat it as a scalar field Scalar waveguide theory has been used to model SAW

waveguides and waveguide resonators [13] Leaky waveshyguide modes have been studied in 112-LiTaO3 [14] and in ST-cut quartz [15] [16] However these approaches are not applicable here because of the nonconvex slowness curshyvature of LSAWs For this reason we resort to a scalar Greenrsquos function theory empirically constructed to mimic the effects of the LSAW slowness curvature The grating waveguide in Fig 8 is chosen as the model

structure It consists of an infinite periodic array of elecshytrodes with an acoustic aperture W and two infinitely wide busbars At the stopband frequencies such a structure well approximates a homogeneous synchronous resonator with


Fig 8 Grating waveguide with infinite busbars

long reflectors Zhang et al [17] have shown that the peshyriodic arrays are from the electrical point of view comshypletely characterized by their harmonic admittance The concept originally proposed for one-dimensional arrays naturally generalizes to grating waveguides

A Scalar Waveguide Model

Let the wavefield be described by a scalar displacement field u(x y) Because of the existence of the device atop the surface scalar surface stresses T (x y) may exist under the metallized surface regions The substrate is described through a Greenrsquos function G(x y) relating the surface displacement and stress via

JJ u(x y) = G(x minus x y minus y)T (x y) dxdy

(2)

Harmonic time dependence at the angular frequency ω = 2πf is assumed and it is included in the fields through an implicit factor of eiωt All fields and quantities are normalshyized The device structure is described through the boundary

conditions The source field S(x y) serves to excite waves and electrical and mechanical perturbations of the surface are described through the load density m(x y) The net boundary condition is

T (x y) = m(x y)ω2 u(x y) + S(x y) (3)

A model for the structure in Fig 8 is obtained with

m(x y) = mW +∆m(y) + 2m1(y) cos(2πxp) (4)

Here the parameter mW measures the loading in the inshyfinitely wide busbars ∆m(y) = m0(y) minus mW and m0(y) and m1(y) describe the uniform and periodic loading proshyfiles in the grating respectively It is practical to define the free stress field

τ(x y mW) equiv T (x y) minus mWω2 u(x y) (5)

which automatically vanishes in the busbars Conseshyquently it must be computed only inside the waveguide

region Expressed through the free stress field the conshystitutive relation in (2) assumes in the Fourier domain the form

u(kx ky) = G(kx ky mW)τ(kx ky mW) (6)

where the mW-loaded Greenrsquos function is

G(kx ky mW) equiv Gminus1(kx ky) minus mWω2

minus1 (7)

We emphasize that the model and in particular the emshypirical Greenrsquos function described subsequently are not proposed as tools for precise analysis but rather as a simshyple method for obtaining meaningful order-of-magnitude estimates on the losses and their dependence on frequency and the device dimensions

B Excitation and Electric Currents

Under harmonic excitation [17] a driving voltage Vn = minusi2πγn V0e is connected to each electrode n The currents

In generated in the electrodes follow the phase of the voltshyminusi2πγn ages such that In = I0e Consequently the ratio

of current and voltage is the same for all electrodes it is known as the harmonic admittance of the array Let Q = 2πp denote the grating wavenumber To

imitate the harmonic excitation in our phenomenological model we postulate a source field of the form

( )minusiγQx + e minusi(γminus1)QxS(x y) = ξ0 sin(πγ) e Θ(W2 minus |y|)

(8)

Here ξ0 is the electromechanical coupling parameter Θ(x) denotes the Heaviside function and W is the electric apershyture Furthermore we assume that the acoustic contribushytion to the harmonic admittance is given as

J +W2

YH(γ f) = iω2ξ0 u(x = 0 y)dy (9) minusW2

Using Fourier transformation techniques the admitshytance of a synchronous resonator with Np active electrode pairs and surrounded by two infinitely long reflectors may be expressed through the harmonic admittance as

J 1 sin2(2πγNp)Y (f) = YH(γ f ) dγ + iωC

0 sin2(2πγ) (10)

Here the capacitance C describes the electrostatic storage of energy in the structure

C Empirical Greenrsquos Function

We now empirically construct an approximate Greenrsquos function that is consistent with the one-dimensional theory from [8] and that with reasonable accuracy produces the slowness curve for fs-BAWs and those for LSAWs under uniform metallization


The one-dimensional Greenrsquos function from [8] is exshytended into two dimensions as follows

minus1

G(kx ky) = PB(kx ky) minus η(kx ky) (11)

Here PB is a function of the form

1 + cξk2k2 y x

PB(kx ky) = k2 + (1 + ν)k2 minus k2 x y B0 1 + ξk2k2

y x (12)

and η is a function of the form

η0kx + minus η1kB0ky

2kx 2

η(kx ky) = (13)1 + η2k2k2

y x

kB0 = ωsB0 where sB0 is the slowness for surface skimshyming fs-BAW η0 is a piezoelectric loading parameter and k+ denotes plusmnkx with the sign chosen such that the real x part is positive The quantitities ν c ξ η1 and η2 are anisotropy parameters The poles of the empirical Greenrsquos function represent

LSAWs on a metallized crystal surface and the branch points ie the zeros of the function PB indicate the slowshynesses of the surface-skimming bulk waves The slowness curves for LSAWs under uniform metallization are found from the equation

Gminus1(kx ky) = mWω2 (14)

Here the loading parameter mW is a monotonic function of the frequency-thickness product hf It may be determined from rigorously computed slownesses for X-propagation sx0(hf) as follows

2 2mW(hf ) = sx0(hf) minus sB0 minus η0sx0(hf) ω

(15)

In practice finding the poles may be reduced to computing the roots of polynomials of s2 The Greenrsquos function pashyy

rameters were determined by fitting the slowness curves to rigorous computations for vanishing metal thickness The resulting approximate slowness curves for the 42-cut are compared with rigorous computations in Fig 5 and an acshyceptable agreement is achieved In addition to the modes shown in Fig 5 the empirical Greenrsquos function may also feature unphysical poles However these are located deep in the complex plane and they are of no relevance to nushymerical simulations

D Numerical Solution

The model is solved numerically using the coupling-ofshymodes (COM) approximation and the boundary element method (BEM) Under the harmonic excitation condition a Floquet expansion of the displacement field yields

+infin minusi(γ+n)Qxu(x y) = un(y)e (16)

n=minusinfin

similarly for the stress and free stress In the COM approxshyimation only the main harmonics (n = 0 and n = minus1) are retained in the expansion Introducing the same notation for the source field S(x y) the boundary conditions in the COM approximation assume the form

τ0(y mW) =∆m(y)ω2u0(y) +m1(y)ω2uminus1(y) + S0(y) τminus1(y mW) =∆m(y)ω2uminus1(y) (17) +m1(y)ω2u0(y) + Sminus1(y)

The constitutive equation is J +W2

un(y) = Gγ+n(y minus y mW)τn(y mW)dy minusW2 (18)

where J1 ˜ minusiky ydkyGγ+n(y mW) = G (Q(γ + n) ky mW) e2π (19)

Substituting (18) into (17) a pair of coupled integral equashytions is found for the free stress field This is solved numerishycally using the BEM for the sake of brevity the details are omitted From the free stress field the displacement field and the harmonic admittance are subsequently found The electrical response of an ideal synchronous resonator is obshytained as a weighted integral of the harmonic admittance

V Electrical Responses

At the stopband frequencies the admittance in (10) should provide a reasonable approximation to the response of a resonator with long reflectors and wide busbars The theory was employed to model the test structure discussed in Section II The profiles m0(y) and m1(y) for uniform and periodic

loading were assumed constants inside the electrically acshytive waveguide region The magnitudes m0 and m1 were determined to yield the correct one-dimensional dispersion relation in the gap between the electrically active region and the busbars the profile functions assumed one-half of these values To describe the losses caused by ss-BAW radiation in the IDT region additional attenuation was introduced using complex-valued frequencies a value of 94 middot 10minus4 Neper per wavelength was extracted from rigshyorous FEM (finite element method)BEM simulations for a one-dimensional structure Resistive losses in the elecshytrodes were estimated to result in an effective series resisshytance of R = 0059Ω The capacitance C was chosen to yield the correct antiresonance frequency The experimental and simulated admittances are comshy

pared in Fig 9 Also shown are the scaled harmonic conshyductance ReYH(05 f) describing a periodic IDT and the conductance obtained for an effectively one-dimensional structure with infinite reflectors and aperture Below the stopband frequencies ideal (infinite) reflectors only poorly


Fig 9 Admittance and conductance of a synchronous test structure on 36YX-cut LiTaO3 vs a two-dimensional resonator model For comparison also the harmonic conductance from a two-dimensional IDT model and the conductance from a one-dimensional resonator model with infinite reflectors are shown

approximate the actual finite reflectors Consequently the conductance oscillations occuring below the resonance are not accurately described by the model However close to the resonance the losses are well reproduced Comparisons of the results from one- and twoshy

dimensional models show agreement with the analysis of the LSAW busbar radiation discussed in Section III The resulting losses are considerable and they well explain the experimentally observed bump in the conductance The small ripples in the experimental conductance in the stopshyband appearing because of resonances of high order transshyverse modes are accurately reproduced in the model However the simulations provide no insight into the

dominant loss mechanism close to the antiresonance Deshyspite the notable increase in the conductance caused by waveguide losses and the radiation of fs-BAWs the simushylated conductance values are only one-fifth of those meashysured experimentally Possible causes for the unidentified losses include the excitation of ss-BAW and acoustic dampshying in the electrodes made of polycrystalline aluminum The contribution of synchronous Rayleigh-wave radiation was investigated by introducing additional poles to the scalar Greenrsquos function but for reasonable values of the coupling the resulting losses were found to be almost negshyligible For frequencies close to and exceeding the threshold

fB asymp 9545 MHz the excitation of fs-BAW becomes the dominant loss mechanism The conductances for test structures with varying metshy

allization ratios (ap = 03 and 07) and apertures (W = 8λ0 and 16λ0) are shown in Fig 10 The substrate is 42shycut LiTaO3 the pitch is p = 4 microm the metal thickness is hλ0 = 8 and the resonators have 75 electrode pairs in the IDTs and 37 electrodes in each reflector Because h and p are the same in all of the structures the quenching of

Fig 10 Experimental and simulated conductances of four test strucshytures with differing metallization ratios ap = 04 and 07 and apershytures W = 8λ0 and 16λ0 on 42YX-cut lithium tantalate also shown are the theoretically estimated frequency thresholds from Fig 7(b)

the LSAW radiation occurs at the same frequency about 503 MHz in all of the structures Another characteristic of the busbar radiation is that in contrast to the admittance caused by LSAW propagation it depends only weakly on the aperture Consequently the losses are relatively more important for narrower structures Finally the S11 parameters of test structures with the

aperture W = 16λ0 are displayed on the Smith chart in Fig 11 for various ap In this display the region of the radiation is denoted by the thick curves Because the stopband changes with ap and the frequency range prone to the busbar radiation remains constant the leakage reshygion appears to rotate clockwise in the chart as a function of the metallization ratio

VI Discussion

We have carried out laser interferometric measurements to study the loss mechanisms in an LSAW resonator on a LiTaO3 substrate The scanned images reveal acousshytic leakage from the active resonator area to the busbars of the device This is identified as LSAWs and Rayleigh waves being radiated to the busbars and transversely exshycited Rayleigh waves The radiation of LSAWs to the busbars strongly deshy

pends on frequency and it may result in significant losses Although the resonance and the antiresonance depend on the width height and shape of the electrodes and the geometry of the structure the frequency characteristics of the busbar radiation are governed by the relative alushyminum thickness in the busbars For the typically emshyployed electrode thicknesses the frequency region in which the side radiation is viable occurs inside the stopband and sometimes even includes the resonance frequency


Fig 11 Measured S11 parameter for test structures with varying metallization ratio ap Thick curves the frequency interval prone to busbar radiation with onset at 494 MHz (square) and quenching at 503 MHz (diamond) For ap = 04 the onset coincides with the resonance for higher values it occurs in the stopband

A phenomenological simulation was constructed to estishymate the losses caused by the LSAW busbar radiation the excitation of the fs-BAWs and LSAW attenuation caused by coupling to ss-BAWs According to the simulations the busbar radiation well explains the experimentally observed increase in the conductance close to the resonance freshyquency Experiments confirm that the magnitude of the radiation depends only weakly on the aperture Conseshyquently relative losses are pronounced for narrow apershytures At high frequencies above the stopband the radiation

of fs-BAWs is the dominant loss mechanism However none of the phenomena studied explains the large magshynitude of the losses observed experimentally close to the antiresonance The residual excitation of slow shear bulk waves and the acoustic attenuation in the aluminum elecshytrodes are among the remaining loss mechanisms that reshyquire investigation Comprehensive experiments or a rigshyorous theoretical simulation may be required to find the means to minimize the losses and thus to optimize the resonator performance

Acknowledgments

The authors are grateful to Clinton S Hartmann and Marc Solal for fruitful discussions

References

[1] K Hashimoto M Yamaguchi S Mineyoshi O Kawachi M Ueda G Endoh and O Ikata ldquoOptimum leaky-SAW cut of

LiTaO3 for minimised insertion loss devicesrdquo in Proc 1997 IEEE Ultrason Symp pp 245ndash254

[2] H H Ou N Inose and N Sakamoto ldquoImprovement of laddershytype SAW filter characteristics by reduction of inter-stage misshymatching lossrdquo in Proc 1998 IEEE Ultrason Symp pp 97ndash 102

[3] V P Plessky D P Chen and C S Hartmann ldquolsquoPatchrsquo imshyprovements to COM model for leaky wavesrdquo in Proc 1994 IEEE Ultrason Symp pp 297ndash300

[4] J V Knuuttila P T Tikka C S Hartmann V P Plessky and M M Salomaa ldquoAnomalous asymmetric acoustic radiation in low-loss SAW filtersrdquo Electron Lett vol 35 pp 1115ndash1116 1999

[5] J V Knuuttila P T Tikka and M M Salomaa ldquoScanshyning Michelson interferometer for imaging surface acoustic wave fieldsrdquo Opt Lett vol 25 pp 613ndash615 2000

[6] J Koskela J V Knuuttila P T Tikka M M Salomaa C S Hartmann and V P Plessky ldquoAcoustic leakage mechanism for leaky SAW resonators on lithium tantalaterdquo Appl Phys Lett vol 75 pp 2683ndash2685 1999

[7] J V Knuuttila J Koskela P T Tikka M M Salomaa C S Hartmann and V P Plessky ldquoAsymmetric acoustic radiation in leaky SAW resonators on lithium tantalaterdquo in Proc 1999 IEEE Ultrason Symp pp 83ndash86

[8] J Koskela V P Plessky and M M Salomaa ldquoTheory for shear horizontal surface acoustic waves in finite synchronous resshyonatorsrdquo IEEE Trans Ultrason Ferroelect Freq Contr vol 47 pp 1550ndash1560 Nov 2000

[9] S V Biryukov Y V Gulyaev V V Krylov and V P Plessky Surface Acoustic Waves in Inhomogeneous Media Springer-Verlag 1995 pp 255ndash259

[10] G Kovacs M Anhorn H E Engan G Visintini and C C W Ruppel ldquoImproved material constants for LiNbO3 and LiTaO3rdquo in Proc 1990 IEEE Ultrason Symp pp 435ndash438

[11] S V Biryukov and M Weihnacht ldquoThe effective permittivity in the complex plane and a simple estimation method for leaky wave slownessrdquo in Proc 1996 IEEE Ultrason Symp pp 221ndash 224

[12] C S Hartmann B P Abbott S Jen and D P Chen ldquoDistorshytion of transverse mode symmetry in SAW transversely coupled resonators due to natural SPUDT effectsrdquo in Proc 1994 IEEE Ultrason Symp pp 71ndash74

[13] H A Haus and K L Wang ldquoModes of a grating waveguiderdquo J Appl Phys vol 49 pp 1061ndash1069 1978

[14] C S Hartmann V P Plessky and S Jen ldquo112-LiTaO3 peshyriodic waveguidesrdquo in Proc 1995 IEEE Ultrason Symp pp 63ndash66

[15] S Rooth and A Roslashnnekleiv ldquoSAW propagation and reflections in transducers behaving as waveguides in sense of supporting bound and leaky moderdquo in Proc 1996 IEEE Ultrason Symp pp 201ndash206

[16] M Solal J V Knuuttila and M M Salomaa ldquoModelling and visualization of diffraction like coupling in SAW transversely coupled resonator filtersrdquo in Proc 1999 IEEE Ultrason Symp pp 101ndash106

[17] Y Zhang J Desbois and L Boyer ldquoCharacteristic parameters of surface acoustic waves in periodic metal grating on a piezoshyelectric substraterdquo IEEE Trans Ultrason Ferroelect Freq Contr vol 40 pp 183ndash192 May 1993

Julius Koskela received the MSc LicTech and DrTech degrees in technical physics at the Helsinki University of Technology (HUT) in 1996 1998 and 2001 respectively His research interests include SAW physics and modeling SAW devices After his doctoral disshysertation he joined the Nokia Group he is currently working at the Nokia Research Censhyter He is a member of the Finnish Physical Society


Jouni V Knuuttila received the MSc deshygree in technical physics at the Helsinki Unishyversity of Technology (HUT) in 1998 He is a postgraduate student in the Materials Physics Laboratory at HUT His research interests include optical imaging of surface and bulk acoustic waves sonoluminescence and audio signal processing He is a member of the Finnish Optical Society

Tapani Makkonen (Mrsquo98) received the MSc degree in technical physics at the Helsinki University of Technology in June 1996 after which he continued to work in the Materishyals Physics Laboratory as a DrTech student His research interests include the modeling of package parasitic effects in SAW devices currently he is focusing on the FEM of crysshytal resonators Makkonen is a member of the Finnish Physical Society

Victor P Plessky (Mrsquo93) received his PhD degree in physical and mathematical sciences at the Moscow Physical-Technical Institute and the DrSc degree at the Institute of Rashydio Engineering and Electronics (IRE Russhysian Academy of Sciences Moscow) in 1978 and 1987 respectively Beginning in 1978 he worked at IRE first as a junior researcher and in 1987 was promoted to the position of Laboratory Director In 1991 he also worked as a part-time professor at the Patris Lushymumba University Moscow He received the

full professor title in 1995 from the Russian Government In 1992 he joined ASCOM Microsystems SA in Bevaix Switzerland where

he worked as a special SAW projects manager He was a visiting professor at the Helsinki University of Technology in April and May 1997 and again in spring 2001 Since 1998 he has been working at Thomson Microsonics (presently Thales Microsonics) He has been engaged in research on semiconductor physics SAW physics (new types of waves scattering and reflection on surface irregularities laser generation of SAW) SAW device development (filters delay lines RACs) and magnetostatic wave studies Currently his intershyests focus on SAW physics and low-loss SAW filter development Prof Plessky is an IEEE member He was awarded the USSR Nashytional Award for Young Scientists in 1984

Martti M Salomaa (Mrsquo94) received his DrTech degree in technical physics from Helsinki University of Technology (HUT) in 1979 Thereafter he worked at UCLA and the University of Virginia From 1982 to 1991 he was the theory group leader at the Low Temshyperature Laboratory HUT and from 1988 to 1991 he served as the director of the ROTA project between the Academy of Finland and the Soviet Academy of Sciences He has held a sabbatical stipend at the University of Karlshysruhe and in 1994 he was a guest professhy

sor at ETH-Zurich Since 1996 he has been a professor of technical physics and the Director of the Materials Physics Laboratory in the Department of Technical Physics and Mathematics at HUT He is a co-recipient of the 1987 Award for the Advancement of European Scishyence (presented by the Korber Foundation Hamburg) His research interests include BEC superfluidity superconductivity magnetism physics of SAW nondiffracting waves nanoelectronics mesoscopic physics and sonoluminescence He is a member of the IEEE APS EPS and the Finnish Physical and Optical Societies


= 120 electrode pairs in the interdigital transducer (IDT) and Ng = 50 electrodes in each reflector The pitch is p = 2214 microm the aperture is W = 70 microm the relative alushyminum electrode thickness is hλ0 = 56 and the metshyallization ratio is about 05 Also shown is a fit to a oneshydimensional phenomenological resonator model [8] which takes into consideration the interactions between LSAWs and fs-BAWs The results are rather typical for the model and LSAW resonators on 36-42YX-LiTaO3 Although the resonance and the dispersion characterisshy

tics are satisfactorily reproduced by the model systematic discrepancies in the conductance representing losses may be observed on the high frequency side of the resonance peak and in the middle of the stopband As the most noshytable consequence the predicted Q value of the antiresoshynance is too high Yet the agreement shown in Fig 1 reshyquires the inclusion of a parasitic series resistance of about 05 Ω a reasonable theoretical estimate would be about one order of magnitude lower Minor differences between the model and the experiments may be explained by the numerous approximations underlying our model but the magnitude of the disagreement rather suggests the exisshytence of additional loss mechanisms To study directly the acoustic activity in LSAW devices

we utilize a scanning optical Michelson interferometer [5] which detects the shear vertical component of the mechanshyical displacement field Fig 2 displays the light reflection data and a wide amplitude scan of the test resonator at the frequency f = 910 MHz coinciding with the unpreshydicted lump in the conductance slightly above the resoshynance peak The resonator is aligned with the crystal Xshyaxis In the longitudinal device direction the acoustic field

remains confined into the active device region as exshypected on the basis of one-dimensional models However the waves are capable of escaping from the device to the busbars At least three separate loss mechanisms may be identified the radiation of LSAWs to the busbars [6] synchronous waveguide radiation of Rayleigh waves [9] at an angle of about 40 and transverse excitation of Rayleigh waves Note that because Rayleigh waves have strong shear vertical polarization and LSAWs are essenshytially shear horizontal surface waves the probe images are likely to strongly pronounce the former over the latter Furthermore it should be kept in mind that mechanisms such as ss-BAW radiation into the bulk and resistive and viscous losses are not revealed from surface scans The observed asymmetry of the probed acoustic field

may be explained by the crystalline anisotropymdashan inshyherent materials propertymdashof the LiTaO3 substrate The LSAW velocity is a symmetric function of the propagation angle θ about the crystal X axis see Fig 2(a) However the LSAW polarization is an asymmetric function of θ and the asymmetry is particularly strong in the shear vertical component detected by the probe [6] The series of probe images in Fig 3 illustrates the deshy

pendence of the LSAW busbar radiation on frequency Below the resonance frequency the phenomenon exists

Fig 2 Areal scan of the test resonator a) Light reflection data b) the shear vertical displacement field at 910 MHz indicating three twoshydimensional leakage mechanisms The displacement is not to scale in the areas with different light reflection coefficients

weakly at frequencies slightly above the resonance it is very pronounced Close to a quenching frequency of about 918 MHz the radiation becomes strongly suppressed and practically disappears Similar frequency dependence may be recognized in the losses in Fig 1 and it may be unshyderstood on the basis of the curvature of loaded slowness curves as will be discussed subsequently

Because of the quenching of the LSAW busbar radiashytion the phenomenon is not likely to be responsible for the residual losses in the middle of the stopband Fig 4 shows the probed field in the resonator at the antiresoshynance In the image the radiation of obliquely propagatshying and transverse Rayleigh waves appear to be the most prominent acoustic loss mechanisms












































(2)



T (x y) = m(x y)ω2 u(x y) + S(x y) (3)










minus1 (7)








(8)


J +W2




0 sin2(2πγ) (10)






minus1



1 + cξk2k2 y x


y x (12)



2kx 2

η(kx ky) = (13)1 + η2k2k2

y x






(15)






n=minusinfin





















VI Discussion







Acknowledgments


References







































































(2)



T (x y) = m(x y)ω2 u(x y) + S(x y) (3)










minus1 (7)








(8)


J +W2




0 sin2(2πγ) (10)






minus1



1 + cξk2k2 y x


y x (12)



2kx 2

η(kx ky) = (13)1 + η2k2k2

y x






(15)






n=minusinfin





















VI Discussion







Acknowledgments


References






























minus1



1 + cξk2k2 y x


y x (12)



2kx 2

η(kx ky) = (13)1 + η2k2k2

y x






(15)






n=minusinfin





















VI Discussion







Acknowledgments


References






































VI Discussion







Acknowledgments


References
































Acknowledgments


References




























acoustic loss mechanisms in leaky saw resonators on lithium...

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